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Symmetry breaking in maximal outerplanar, regular and Cayley graphs Alikhani, Saeid


The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has a vertex (edge) labeling with $d$ labels that is preserved only by a trivial automorphism. In this talk we consider the maximal outerplanar graphs (MOP graphs) and show that MOP graphs, except $K_3$, can be distinguished by at most two vertex (edge) labels. We also consider the distinguishing number and distinguishing index of regular and Cayley graphs. In particular, we present a family of Cayley graphs, graphical regular representations of a group, for which the distinguishing number and the distinguishing index is two. Coauthor: Samaneh Soltani

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